Scroll compressor

ABSTRACT

A scroll compressor is provided. The scroll compressor may include guide holes formed at one of a wrap portion or a base portion, and guide pins inserted into the guide holes formed at the other of the wrap portion or the base portion to couple the wrap portion and the base portion to each other. Such guide pins and guide holes may be easily processed to reduce fabrication costs and reduce or eliminate unstable behavior of the orbiting scroll. As the guide pins and the guide holes have a circular cross section, abrasion of the guide pins or the guide holes may be prevented.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application claims priority under 35 U.S.C. §119 to Korean Application No. 10-2011-0116640 filed on Nov. 9, 2011, whose entire disclosure is hereby incorporated by reference.

BACKGROUND

1. Field

This relates to a scroll compressor, and particularly, to a scroll compressor having a separation-type orbiting scroll.

2. Background

A scroll compressor may compress a refrigerant gas by changing a volume of compression chambers formed by a pair of scrolls facing each other. When compared with a reciprocating compressor or a rotary compressor, the scroll compressor may have higher efficiency, lower vibration and noise, smaller size and lighter weight.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments will be described in detail with reference to the following drawings in which like reference numerals refer to like elements wherein:

FIG. 1 is a sectional view of a scroll compressor according to an embodiment as broadly described herein;

FIG. 2 is a partial cutaway view of a mechanical compression part of the scroll compressor shown in FIG. 1;

FIG. 3 is a disassembled perspective view of an orbiting scroll of the scroll compressor shown in FIG. 1;

FIG. 4 is a sectional view of an orbiting scroll of the scroll compressor shown in FIG. 1;

FIGS. 5 to 7 are planar views illustrating operation of the scroll compressor shown in FIG. 1, and

FIG. 8 is a sectional view and FIG. 9 is a planar view of a wrap portion of an orbiting scroll, illustrating the position of a back pressure chamber of the scroll compressor shown in FIG. 1.

DETAILED DESCRIPTION

Description will now be given in detail of exemplary embodiments, with reference to the accompanying drawings. For the sake of brief description with reference to the drawings, the same or equivalent components will be provided with the same reference numbers, and description thereof will not be repeated.

Scroll compressors may be categorized into a low-pressure scroll compressors or high-pressure scroll compressors according to a type of refrigerant is supplied into the compression chambers. In a low-pressure scroll compressor, refrigerant is indirectly sucked into compression chambers via an inner space of a casing which is divided into a suction space and a discharge space. In a high-pressure scroll compressor, refrigerant is directly sucked into compression chambers without passing through an inner space of the casing, and is then discharged to a discharge space in the inner space of the casing.

Scroll compressors may be also categorized into tip seal type or back pressure type scroll compressors according to a sealing method of the compression chambers. In the tip seal type scroll compressor, a tip seal is installed at the wrap end of each scroll, and the tip seal is levitated when the compressor is driven, causing the levitated tip seal to adhere to a plate portion of the opposite scroll. In the back pressure type scroll compressor, a back pressure chamber is formed on a rear surface of a first scroll, and oil or refrigerant having an intermediate pressure is guided into the back pressure chamber. Then, the first scroll is adhered to a second scroll facing the first scroll by pressure in the back pressure chamber. Generally, the tip seal method is applied to a low-pressure scroll compressor, whereas the back pressure method is applied to a high-pressure scroll compressor.

The scroll compressor performs an orbit motion with two side surfaces of an orbiting scroll in an axial direction contacting a fixed scroll and a main frame, respectively. Precise manufacture/processing of the orbiting scroll may minimize/eliminate vibration of the orbiting scroll and minimize frictional losses. To this end, a bearing surface contacting the main frame may be processed first, and then a wrap may be processed. However, this may be relatively time consuming, and the bearing surface may be damaged when the wrap portion is processed. Further, design and fabrication of the orbiting scroll may be relatively complicated due to the shapes of the orbiting scroll and the fixed scroll, and in particular, the shape and the size of the wrap portion may be variable according to the capacity of the compressor.

Additionally, a frictional force between the bearing surface of the fixed scroll and the bearing surface of the orbiting scroll may be variable according to a pressure applied to the back pressure chamber. Accordingly, in order to prevent refrigerant leakage and to reduce frictional force, the pressure applied to the back pressure chamber may be properly maintained. A relatively high pressure may be applied to the back pressure chamber, because the orbiting scroll of the scroll compressor is supported by the pressure in the back pressure chamber. Further, when the pressure in the back pressure chamber is varied, sealing performance between the orbiting scroll and the fixed scroll may be consistent. Especially, the pressure in the back pressure chamber may be influenced by a discharge pressure, and the discharge pressure may vary according to a load applied to the compressor. Therefore, a sealing function and frictional loss between the orbiting scroll and the fixed scroll may be influenced by the change of a load applied to the compressor.

As shown in FIGS. 1 to 3, a scroll compressor as embodied and broadly described herein may include a case 1 having an inner space divided into a suction space 11 (low pressure part) and a discharge space 12 (high pressure part), a driving motor 2 for providing a rotational force to the suction space 11 of the case 1, and a main frame 3 fixedly-installed between the suction space 11 and the discharge space 12 of the case 1.

A fixed scroll 4 is fixedly-installed on an upper surface of the main frame 3. An orbiting scroll 5, which forms a pair of compression chambers (P) that consecutively move together with the fixed scroll 4 by being eccentrically-coupled to a crank shaft 23 of the driving motor 2, is installed between the main frame 3 and the fixed scroll 4 so as to perform an orbiting motion. An Oldham's ring 6 for preventing rotation of the orbiting scroll 5 may be installed between the main frame 3 and the orbiting scroll 5.

A suction pipe 13 may be coupled to the suction space 11 of the case 1 so as to be communicated therewith, and a discharge pipe 14 may be coupled to the discharge space 12 so as to be communicated therewith. As discussed above, the inner space of the case 1 may be divided into a suction space (low pressure part) and a discharge space (high pressure part), in certain embodiments by a discharge plenum forming the sealed discharge space 12 and fixedly-coupled to the fixed scroll 4. Alternatively, the inner space of the case 1 may be divided into a suction space and a discharge space by a high-low pressure separation plate fixed to an upper surface of the fixed scroll 4 and adhered to an inner circumferential surface of the case 1.

The fixed scroll 4 may be provided with a fixed wrap 42 protruding from a corresponding surface of a plate portion 41 and formed in an involute shape so as to form the compression chambers (P) together with an orbiting wrap 52 protruding from a wrap portion 50 of the orbiting scroll 5. A suction opening may be formed on an outer circumferential surface of the plate portion 41 of the fixed scroll 4, so that the suction space 11 of the case 1 may communicate with the compression chambers (P). A discharge opening 44 may be formed at a central part of the plate portion 41 of the fixed scroll 4, so that the discharge space 12 of the case 1 may communicate with the compression chambers (P).

The scroll compressor may also include a sub-frame 7, a discharge valve 8, a stator 21 and a rotor 22.

In a scroll compressor as embodied and broadly described herein, refrigerant may be introduced into the suction space 11 (low pressure part) of the case 1 through the suction pipe 13 from a refrigerating cycle. Then, the low-pressure refrigerant in the suction space 11 is introduced into the compression chambers through the suction opening of the fixed scroll 4, and moves to a central part of the orbiting scroll 5 and the fixed scroll 4 by the orbiting scroll 5. Then, the refrigerant is compressed to be discharged to the discharge space 12 of the case 1 through the discharge opening 44 of the fixed scroll 4. Such processes are repeatedly performed.

The orbiting scroll 5 may form the compression chambers (P) which move towards the center of the orbiting scroll 5 while performing an orbiting motion while engaged with the fixed scroll 4. The compression chambers may have a relatively high pressure towards the discharge side, i.e., the final compression chamber side corresponding to the central part. As the compression chambers have a high pressure, a gas repulsive force may be generated that pushes the fixed scroll 4 and the orbiting scroll 5 in a radial direction.

In this situation, this force may push on the fixed scroll 4, but the fixed scroll 4 does not move in a radial direction since it is fixed to the main frame 3 by bolts. On the other hand, the orbiting scroll 5 may be moved with respect to the fixed scroll 4 in a radial direction, since it is installed between the main frame 3 and the fixed scroll 4 so as to rotate together with the crank shaft 23.

Gaps may be generated between the distal ends of the wraps of the compression chambers and the respective plate portions. This may increase leakage of refrigerant in an axial direction. Accordingly, a tip seal may be installed at the distal end of the wrap. Alternatively, a back pressure chamber may be formed on a rear surface of the orbiting scroll 5 so that the orbiting scroll 5 may be substantially entirely supported in an axial direction by pressure obtained as part of compression gas is bypassed. In the latter case, a relatively large amount of high-pressure gas may be required to adequately support the entire orbiting scroll 5. Accordingly, a large amount of compression gas may be leaked to the back pressure chamber from the compression chambers. However, this may degrade compressor performance, or may lower the reliability of the compressor since the orbiting scroll is not uniformly supported by the pressure in the back pressure chamber.

Accordingly, a scroll compressor as embodied and broadly described herein may include a separation-type orbiting scroll having a back pressure chamber formed between two parts of the orbiting scroll. When so configured, a gap between the fixed scroll and the orbiting scroll may be substantially completely sealed by a relatively low pressure.

For instance, the orbiting scroll 5 may include the wrap portion 50 engaged with the fixed scroll 4, and a base portion 60 coupled to the wrap portion 50.

The wrap portion 50 may include the orbiting wrap 52 which forms compression chambers by engagement with the fixed wrap 42, and a wrap flange 54 integrally formed with the orbiting wrap 52. The wrap flange 54 may have a disc shape.

The base portion 60 may be coupled to the wrap portion 50, facing the bottom surface of the wrap flange 54. More specifically, the base portion 60 may include a base flange 64 having a disc shape in a similar manner to the wrap flange 54, and a boss portion 68 formed on the bottom surface of the base flange 64 and coupled to the crank shaft 23.

A plurality of guide pins 66 slidably inserted into guide holes 58 formed in the wrap portion 50 may be formed on the edge of the upper surface of the base flange 64. As the guide pins 66 are slidably inserted into the guide holes 58 in an axial direction, the wrap portion 50 may be moved with respect to the base portion 60 in an axial direction of the crank shaft 23. However, in this case, the wrap portion 50 cannot be moved in a radial direction or a circumferential direction of the crank shaft 23. Since the movement of the wrap portion 50 in an axial direction is restricted by a gap between the fixed scroll 4 and the main frame 3, the guide pins 66 may remain inserted into the guide holes 58. That is, the wrap portion 50 and the base portion 60 may be stably coupled to each other just as the guide pins 66 are inserted into the guide holes 58, without using a bolt-coupling method or a welding method.

Since the guide pins 66 and the guide holes 58 are easily processed, fabrication costs may be reduced. Further, since the guide pins 66 and the guide holes 58 are precisely processed, unstable behavior of the orbiting scroll 5 may be prevented. Since the guide pins 66 and the guide holes 58 are formed to have a circular cross section, abrasion of the guide pins 66 or the guide holes 58 may be prevented because a load applied to the guide pins 66 is uniformly distributed even if the base portion 60 transfers a driving force of the driving motor 2 to the wrap portion 50.

The Oldham's ring 6, serving as a rotation preventing device, may be coupled to the bottom surface of the base portion 60. More specifically, the Oldham's ring 6 may include a ring-shaped portion 6 a contacting the bottom surface of the base flange 64. First protrusions 6 b having a phase difference of 180° from each other may be formed at two sides of the bottom surface of the ring-shaped portion 6 a. The first protrusions 6 b may be inserted into first protrusion recesses 3 a of the main frame 3. Second protrusions 6 c having a phase difference of 180° from each other may be formed at two sides of the upper surface of the ring-shaped portion 6 a. The second protrusions 6 c may be inserted into second protrusion recesses 64 a formed on the bottom surface of the base flange 64, respectively.

When so configured, even if a rotational force of the crank shaft 23 is transferred to the base portion 60, the base portion 60 performs an orbit motion without being rotated, and the wrap portion 50 coupled to the base portion 60, which is prevented from moving in a radial direction, also performs an orbit motion together with the base portion 60.

A back pressure chamber 62 having a seal 62 a may be formed on the upper surface of the base flange 64. Referring to FIG. 4, the back pressure chamber 62 may be formed between the bottom surface of the wrap flange 54 and the upper surface of the base flange 64. The inner space of the back pressure chamber 62 may be separated from the suction space 11 (low pressure part) by the seal 62 a inserted into and fixed to the base flange 64. A back pressure hole 54 a for communicating the inner space of the back pressure chamber 62 with the compression chambers (P) may penetrate the base flange 64.

Accordingly, refrigerant compressed in the compression chambers may be partially introduced into the back pressure chamber through the back pressure hole 54 a. Since the inner pressure of the back pressure chamber 62 is higher than the peripheral pressure of the base flange 64, the wrap portion 50 is prevented from moving upward from the base portion 60 in an axial direction. Further, this may prevent bending of a central part of the wrap portion 50 towards the base portion 60 due to a pressure of the compression chambers. When so figured, a gap between the bottom surface of the fixed scroll 4 and the orbiting wrap 52 may be sealed.

The inner pressure of the back pressure chamber 62 may be determined according to the position of the back pressure hole 54 a. That is, as the back pressure hole 54 a moves close to the center of the orbiting wrap 52 of the orbiting scroll 5, the pressure in the back pressure chamber 62 increases. On the other hand, as the back pressure hole 54 a moves towards the outside of the orbiting wrap 52 of the orbiting scroll 5, the pressure in the back pressure chamber 62 decreases.

FIGS. 5 to 7 are planar views of the wraps 42 and 52, illustrating a process in which a refrigerant is compressed by the orbiting wrap 52 and the fixed wrap 42. Referring to FIG. 7, as a pressure in a final compression chamber reaches a discharge pressure, a discharge operation is initiated. As aforementioned, the pressure in the compression chambers formed by the orbiting wrap and the fixed wrap continuously changes during a compression operation. Accordingly, a pressure at any point on the orbiting wrap also continuously changes in a single compression cycle.

For instance, if the back pressure hole 54 a is positioned at ‘a’, the same pressure as a discharge pressure is applied to the back pressure chamber 62, because the point ‘a’ is a position where a discharge pressure is maintained during a compression operation. In this case, a strong thrust force (frictional force in an axial direction) is generated between the bottom surface of the fixed scroll and the orbiting wrap due to an excessive back pressure. This may cause frictional loss to be increased. Further, a discharge pressure is variable according to the amount of a compression load applied to the compressor. Accordingly, if the back pressure hole 54 a is formed at the point ‘a’ where a discharge pressure is continuously applied, the frictional force in an axial direction (thrust force) is variable according to a load. This may influence the performance of the compressor. More specifically, the point ‘a’ is within the range of a discharge starting angle (hereinafter, will be referred to as ‘α’).

Referring to FIG. 6, the point ‘b’ is a position where a discharge pressure is applied for a predetermined time duration during a compression operation, and an intermediate pressure between a suction pressure and a discharge pressure is applied for the remaining time duration. Accordingly, if the back pressure hole 54 a is formed at the point ‘b’, a proper back pressure may be obtained, and a discharge pressure changed by the change of a load, etc. may be attenuated by the intermediate pressure. The present inventor has certified that the point ‘b’ is within the range of 180°, from the discharge starting angle of the orbiting wrap, i.e., ‘α+180’.

As shown in FIG. 7, the point ‘c’ is a point where only an intermediate pressure is continuously applied during a compression operation. Accordingly, if a back pressure hole 54 a is formed at the point ‘c’, a back pressure is too low and there may be difficulty in obtaining sufficient sealing. This may cause leakage of refrigerant.

When compressing a refrigerant while performing an orbit motion, a non-uniform moment may be applied to the orbiting scroll 5 due to a gas repulsive force. If the non-uniform moment is not effectively reduced, the orbiting scroll 5 may experience unstable behavior. This may increase frictional loss or abrasion between the orbiting scroll 5 and the fixed scroll 4, or between the orbiting scroll 5 and the main frame 3, or between the wrap portion 50 and the base portion 60. This may lower the reliability and/or performance of the compressor.

In embodiments as broadly described herein, the center of the back pressure chamber 62 which supports the orbiting scroll 5 in an axial direction may be eccentrically positioned at a point where a non-uniform moment is the greatest. This may prevent unstable behavior of the orbiting scroll 5. Generally, a non-uniform moment occurring on the orbiting scroll 5 while the crank shaft 23 performs a single rotation may be greatest when refrigerant is discharged. Therefore, in order to effectively reduce the non-uniform moment, the center of the back pressure chamber 62 may be positioned at a point where refrigerant starts to be discharged.

Referring to FIGS. 8 and 9, it is assumed that a line which connects a geometric center (B) of the orbiting scroll 5 with a rotation center (axial center) (C) of the crank shaft 23 is a first virtual line (L1), and a line perpendicular to the first virtual line (L1) is a second virtual line (L2). Under such assumption, a gas repulsive force is applied to the orbiting scroll 5 in a direction of the second virtual line (L2), a direction resistive to rotation.

The center (O) of the back pressure chamber 62 may be eccentric from the geometric center (B) of the orbiting scroll 5 by a predetermined gap, so as to be positioned within the range of ±30° from the second virtual line (L2) positioned on the opposite side to a direction where a gas repulsive force is applied, preferably, so as to be positioned on the second virtual line (L2) where a gas repulsive force is applied.

In a scroll compressor as embodied and broadly described herein, the wrap portion and the base portion are coupled to each other by a plurality of pins and a plurality of guide holes. The guide pins, and the guide holes for inserting the guide pins are easily processed, thereby reducing the fabricating costs. Further, since the guide pins and the guide holes are precisely processed, unstable behavior of the orbiting scroll may be prevented. Further, since the guide pins and the guide holes have a circular cross section, abrasion of the guide pins or the guide holes may be prevented.

A scroll compressor is provided including an easily fabricated orbiting scroll.

A scroll compressor is provided that is capable of minimizing frictional loss between an orbiting scroll and a fixed scroll, and capable of obtaining a sufficient sealing performance even if a load changes.

A scroll compressor as embodied and broadly described herein may include a case; a fixed scroll installed in the case; a wrap portion configured to form compression chambers by being engaged with the fixed scroll; a base portion coupled to the wrap portion, and configured to support the wrap portion so as to be movable towards the fixed scroll; a driving motor coupled to a rear surface of the base portion, and configured to eccentrically rotate the base portion and the wrap portion; and a main frame installed in the case, and configured to support the base portion in an axial direction, wherein a plurality of guide pins are formed at one of the wrap portion and the base portion in an axial direction, and guide holes for slidably inserting the guide pins in an axial direction are formed at another thereof.

A scroll compressor according to another embodiment as broadly described herein may include comprising: a fixed scroll having a fixed wrap; and an orbiting scroll having an orbiting wrap and performing an orbit motion with respect to the fixed scroll, in which a pair of compression chambers that consecutively move are formed between the orbiting scroll and the fixed scroll, wherein the orbiting scroll is divided into at least two parts in an axial direction, and wherein a plurality of guide pins are formed at one of the divided parts in an axial direction, and guide holes for slidably inserting the guide pins in an axial direction are formed at another of the divided parts.

Any reference in this specification to “one embodiment,” “an embodiment,” “example embodiment,” etc., means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. The appearances of such phrases in various places in the specification are not necessarily all referring to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection with any embodiment, it is submitted that it is within the purview of one skilled in the art to effect such feature, structure, or characteristic in connection with other ones of the embodiments.

Although embodiments have been described with reference to a number of illustrative embodiments thereof, it should be understood that numerous other modifications and embodiments can be devised by those skilled in the art that will fall within the spirit and scope of the principles of this disclosure. More particularly, various variations and modifications are possible in the component parts and/or arrangements of the subject combination arrangement within the scope of the disclosure, the drawings and the appended claims. In addition to variations and modifications in the component parts and/or arrangements, alternative uses will also be apparent to those skilled in the art. 

What is claimed is:
 1. A scroll compressor, comprising: a case; a fixed scroll installed in the case; an orbiting scroll installed in the case and engaged with the fixed scroll, the orbiting scroll comprising: a wrap portion configured engage the fixed scroll to form compression chambers therebetween; a base portion coupled to the wrap portion and configured to be movable towards the fixed scroll to support the wrap portion; a plurality of guide pins provided at one of the wrap portion or the base portion, the plurality of guide pins extending in an axial direction of the wrap portion and the base portion; and a corresponding plurality of guide holes formed in the other of the wrap portion or the base portion, the plurality of guide holes extending in the axial direction of the wrap portion and the base portion, at positions respectively corresponding to the plurality of guide pins, such that the plurality of guide pins are slidably received in the plurality of guide holes; a driving motor coupled to the base portion and configured to eccentrically rotate the base portion and the wrap portion; and a main frame installed in the case and configured to support the base portion.
 2. The scroll compressor of claim 1, wherein each of the plurality of guide pins has a curved outer circumferential surface, and each of the plurality of guide holes has a cross-sectional shape corresponding to its respective guide pin.
 3. The scroll compressor of claim 1, further comprising a back pressure chamber formed between the wrap portion and the base portion, and in communication with the compression chambers.
 4. The scroll compressor of claim 1, further comprising a ring shaped seal provided between the wrap portion and the base portion, wherein the back pressure chamber is formed within in a space defined by the seal.
 5. The scroll compressor of claim 1, wherein the base portion comprises: a boss coupled to a rotation shaft of the driving motor; and a base flange extending radially outward from the boss, facing the wrap portion, wherein the back pressure chamber is formed on a surface of the base flange facing the wrap portion.
 6. The scroll compressor of claim 1, wherein the wrap portion comprises: a wrap flange having a first surface facing the base portion; and an orbiting wrap extending from a second surface of the wrap flange, opposite the first surface thereof, and engaged with a fixed wrap of the fixed scroll; and a back pressure hole extending through the wrap flange to provide for communication between the back pressure chamber and the compression chambers.
 7. The scroll compressor of claim 6, wherein the back pressure hole is formed at a position on the wrap flange where a discharge pressure, and an intermediate pressure between a discharge pressure and a suction pressure, are applied to the back pressure chamber.
 8. The scroll compressor of claim 7, wherein the back pressure hole is formed at a point which is greater than a discharge starting angle and less than the discharge starting angle plus 180 degrees.
 9. The scroll compressor of claim 1, further comprising a plurality of keys integrally formed on one of the wrap portion or the base portion, and a corresponding plurality of key grooves formed in the other of the wrap portion or the base portion and respectively coupled with the plurality of keys.
 10. The scroll compressor of claim 1, wherein an interior of the case is divided into a first space and a second space, the first and second spaces having different pressures, and wherein the wrap portion and the base portion are installed in the first space, the pressure of the first space being lower than that of the second space.
 11. A scroll compressor, comprising: a fixed scroll having a fixed wrap; and an orbiting scroll having an orbiting wrap that is engaged with the fixed wrap such that a pair of compression chambers are formed between the orbiting scroll and the fixed scroll, wherein the pair of compression chambers move as the orbiting scroll orbits with respect to the fixed scroll, wherein the orbiting scroll includes at least a first part and a second part arranged in an axial direction, and wherein a plurality of guide pins are formed on one of the first part or the second part, extending in the axial direction, and a corresponding plurality of guide holes are formed in the other of the first part or the second part, extending in the axial direction, and wherein the plurality of guide pins are slidably received in the plurality of guide holes to couple the first part and the second part.
 12. The scroll compressor of claim 11, wherein each of the plurality of guide pins has a curved outer circumferential surface, and each of the plurality of guide holes has a cross-sectional shape corresponding to its respective guide pin.
 13. The scroll compressor of claim 12, further comprising a back pressure chamber formed between the first and second parts of the orbiting scroll for receiving refrigerant from the pair of compression chambers, wherein a geometric center of the back pressure chamber is eccentric from a geometric center of the orbiting scroll.
 14. The scroll compressor of claim 11, further comprising a ring shaped seal provided between the first and second parts of the orbiting scroll, wherein the back pressure chamber is formed within a periphery of the seal.
 15. The scroll compressor of claim 12, further comprising a back pressure hole formed in one of the first part or the second part, at a position corresponding to the pair of compression chambers, wherein the back pressure hole provides for communication between the back pressure chamber and the pair of compression chambers.
 16. The scroll compressor of claim 13, wherein the back pressure hole is formed at a position where a discharge pressure, and an intermediate pressure between a discharge pressure and a suction pressure, are applied to the back pressure chamber.
 17. The scroll compressor of claim 14, wherein the back pressure hole is formed at a point on the orbiting wrap that is greater than a discharge starting angle and less than the discharge starting angle plus 180 degrees. 